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A325877
Number of strict integer partitions of n such that every orderless pair of distinct parts has a different sum.
20
1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 12, 14, 18, 19, 26, 28, 36, 37, 50, 52, 67, 68, 89, 94, 115, 121, 151, 160, 195, 200, 247, 265, 312, 329, 386, 418, 487, 519, 600, 640, 742, 792, 901, 978, 1088, 1185, 1331, 1453, 1605, 1729, 1925, 2101, 2311, 2524, 2741, 3000
OFFSET
0,4
COMMENTS
The non-strict case is A325857.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..450
EXAMPLE
The a(1) = 1 through a(10) = 9 partitions (A = 10):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (A)
(21) (31) (32) (42) (43) (53) (54) (64)
(41) (51) (52) (62) (63) (73)
(321) (61) (71) (72) (82)
(421) (431) (81) (91)
(521) (432) (532)
(531) (541)
(621) (631)
(721)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&UnsameQ@@Plus@@@Subsets[Union[#], {2}]&]], {n, 0, 30}]
CROSSREFS
The subset case is A196723.
The maximal case is A325878.
The integer partition case is A325857.
The strict integer partition case is A325877.
Heinz numbers of the counterexamples are given by A325991.
Sequence in context: A069911 A185225 A027196 * A100928 A240671 A034140
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 02 2019
STATUS
approved